One can express the inequality \(\theta (\varphi _\mathfrak {C}(\mathcal {O}_C))>0\)  abstractly via [1]}, a consequence of which is
\(\theta \big (\varphi _{\mathfrak {C}}(\mathcal {O}_C)\big )=\sum _\rho \deg (\mathcal {R}_\rho |_C)\theta (\rho ).\) 
